Question

On selling a T. V. at 5% gain and a fridge at 10%gain , a shopkeeper gains rs 2000 . But if he sells the T. V. at 10% gain and fridge at 5% loss. He gains rs 1500 on the transaction. Find the actual prices of T. V. and fridge.

Answer 1

Let the cost price of a TV be x and the cost price of a fridge be y :

When the TV is sold at 5% gain and fridge at 10% gain the profits will be 0.05x and 0.1 y respectively.

0.1y + 0.05x = 2000

When he sells the TV at a gain of 10% and the fridge at 5% loss the profit and loss respectively is 0.10x and 0.05y

0.1x - 0.05y = 1500

We have two simultaneous equations as follows :

0.1x - 0.05y = 1500

0.05x + 0.1y = 2000

Solving simultaneously we have :

0.2x - 0.1y = 3000

0.05x + 0.1y = 2000

0.25x = 5000

x = 5000/0.25 = Rs 20000

Solving for y :

0.05 × 20000 + 0.1y = 2000

1000 + 0.1y = 2000

0.1y = 1000

y = Rs 10000